Question
A blue and a green billiard ball, each with a mass of 0.15 kg, collide head on. Before the collision, the blue ball had a speed of 3 m/s while the green ball had a speed of 2 m/s in the opposite direction. After the collision, the blue ball stays in place while the green ball continues in motion.
In 3-4 sentences, represent the situation before and after the collision and calculate the speed of the green ball after the collision. Be sure to discuss direction.
In 3-4 sentences, represent the situation before and after the collision and calculate the speed of the green ball after the collision. Be sure to discuss direction.
Answers
GPT-4o mini
Before the collision, the blue billiard ball (0.15 kg) is moving at a speed of 3 m/s to the right, while the green billiard ball (0.15 kg) is moving at a speed of 2 m/s to the left (in the opposite direction). After the collision, the blue ball comes to a complete stop, remaining in place, and the green ball continues to move to the left.
To find the speed of the green ball after the collision, we can use the principle of conservation of momentum. The total momentum before the collision is given by:
\[
\text{Momentum}_{initial} = m_{blue} \cdot v_{blue} + m_{green} \cdot v_{green} = (0.15 \, \text{kg} \cdot 3 \, \text{m/s}) + (0.15 \, \text{kg} \cdot (-2 \, \text{m/s})) = 0.45 \, \text{kg m/s} - 0.30 \, \text{kg m/s} = 0.15 \, \text{kg m/s}.
\]
After the collision, the blue ball is stationary, so its momentum contribution is 0. Therefore, the momentum of the green ball must equal the initial total momentum:
\[
0.15 \, \text{kg m/s} = 0.15 \, \text{kg} \cdot v_{green, final}.
\]
Solving for \( v_{green, final} \):
\[
v_{green, final} = \frac{0.15 \, \text{kg m/s}}{0.15 \, \text{kg}} = 1 \, \text{m/s}.
\]
This means the green ball moves to the left with a speed of 1 m/s after the collision.
To find the speed of the green ball after the collision, we can use the principle of conservation of momentum. The total momentum before the collision is given by:
\[
\text{Momentum}_{initial} = m_{blue} \cdot v_{blue} + m_{green} \cdot v_{green} = (0.15 \, \text{kg} \cdot 3 \, \text{m/s}) + (0.15 \, \text{kg} \cdot (-2 \, \text{m/s})) = 0.45 \, \text{kg m/s} - 0.30 \, \text{kg m/s} = 0.15 \, \text{kg m/s}.
\]
After the collision, the blue ball is stationary, so its momentum contribution is 0. Therefore, the momentum of the green ball must equal the initial total momentum:
\[
0.15 \, \text{kg m/s} = 0.15 \, \text{kg} \cdot v_{green, final}.
\]
Solving for \( v_{green, final} \):
\[
v_{green, final} = \frac{0.15 \, \text{kg m/s}}{0.15 \, \text{kg}} = 1 \, \text{m/s}.
\]
This means the green ball moves to the left with a speed of 1 m/s after the collision.
goku
In 3 sentences
GPT-4o mini
Before the collision, the blue billiard ball (0.15 kg) moves to the right at 3 m/s, while the green billiard ball (0.15 kg) moves to the left at 2 m/s. After the collision, the blue ball comes to a complete stop, and the green ball continues moving to the left. Using conservation of momentum, we find that the speed of the green ball after the collision is 1 m/s to the left.
goku
Like a 10th grader
GPT-4o mini
Before the collision, the blue billiard ball, which weighs 0.15 kg, is moving to the right at 3 m/s, and the green billiard ball, also 0.15 kg, is moving to the left at 2 m/s. After the collision, the blue ball stops, and the green ball keeps moving to the left. By using the conservation of momentum, we calculate that the speed of the green ball after the collision is 1 m/s to the left.